Predictive Coding Framework Unified with Bayesian Optimization via Proximal Gradients
Researchers have recast predictive coding — a prominent theory of brain computation — as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. The work shows that a single-level version of this framework precisely recovers the leaky firing-rate neural circuit proposed by Rao and Ballard, with the prior distribution selecting the network's nonlinearity via its proximal operator. The result provides a unified optimization-theoretic foundation for hierarchical predictive coding and clarifies how Bayesian priors shape neural circuit properties.
A technical report submitted to arXiv by Francesco Bullo and colleagues derives predictive coding networks from a single optimization principle: continuous-time proximal gradient descent on a regularized MAP objective. At the single-level, the analysis shows that the membrane leak, recurrent connectivity, synaptic drive, and static nonlinearity of a leaky firing-rate network all emerge naturally from this framework, reproducing the Rao-Ballard circuit. For hierarchical networks, the authors apply a classical variable-splitting relaxation to the deep MAP problem, yielding hierarchical predictive coding as an interconnection of local and distributed solvers. In probabilistic terms, this relaxation converts the directed generative chain into an undirected Markov random field, with each level's node potential defined by its level-wise prior. Each level then applies an activation function equal to the proximal operator of its respective prior, providing a principled mechanism by which different priors can produce different nonlinearities across the hierarchy.
What's missing
The paper is a technical report and has not yet undergone peer review. It does not empirically validate the derived circuits against neurophysiological data or benchmark the framework against alternative theoretical accounts of predictive coding. The scope of the variable-splitting relaxation's approximation quality — and whether the undirected Markov random field faithfully captures the original directed generative model in practice — is not fully characterized.
What different sources said
- arXiv cs.LGCenter
Predictive Coding with Bayesian Priors via Proximal Gradients
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